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arXiv 2402.05052cs.LGstat.ML
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多分布下的因果表示学习:一种通用设定

Causal Representation Learning from Multiple Distributions: A General Setting

Carnegie Mellon University(卡内基梅隆大学);Mohamed bin Zayed University of Artificial Intelligence(穆罕默德·本·扎耶德人工智能大学)

Kun Zhang, Shaoan Xie, Ignavier Ng, Yujia Zheng

AI总结:

本文提出一种完全非参数的多分布因果表示学习通用设定,在潜在图稀疏性和因果影响充分变化条件下,可恢复底层DAG的道德化图,部分场景下能恢复多数潜在变量,实验验证了理论结论。

摘要:

在许多问题中,观测变量(如图像像素)只是潜在因果变量(如底层概念或对象)的数学函数。为了在变化环境中进行预测或对系统做出适当调整,恢复潜在因果变量$Z_i$及其由图$\u2702\tilde{G}_Z$表示的因果关系是很有帮助的。该问题近年来被称为因果表示学习。本文研究一种通用的完全非参数设定下的多分布因果表示学习(分布来自异质数据或非平稳时间序列),不假设分布变化背后存在硬干预。我们旨在为这一基础场景开发通用解决方案;作为副产品,这有助于理解参数化因果模型或硬干预等其他假设带来的独特优势。我们证明,在潜在变量恢复图的稀疏性约束以及因果影响满足合适的充分变化条件下,有趣的是,人们可以恢复底层有向无环图的道德化图,且恢复的潜在变量及其关系与底层因果模型以特定的非平凡方式相关联。在某些情况下,大多数潜在变量甚至可以在分量变换的意义下被恢复。实验结果验证了我们的理论结论。

英文摘要:

In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or making proper changes to the system, it is helpful to recover the latent causal variables $Z_i$ and their causal relations represented by graph $\mathcal{G}_Z$. This problem has recently been known as causal representation learning. This paper is concerned with a general, completely nonparametric setting of causal representation learning from multiple distributions (arising from heterogeneous data or nonstationary time series), without assuming hard interventions behind distribution changes. We aim to develop general solutions in this fundamental case; as a by product, this helps see the unique benefit offered by other assumptions such as parametric causal models or hard interventions. We show that under the sparsity constraint on the recovered graph over the latent variables and suitable sufficient change conditions on the causal influences, interestingly, one can recover the moralized graph of the underlying directed acyclic graph, and the recovered latent variables and their relations are related to the underlying causal model in a specific, nontrivial way. In some cases, most latent variables can even be recovered up to component-wise transformations. Experimental results verify our theoretical claims.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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